The oak and glass door has lots of trim and not all the wood matches exactly, which is great. Should I choose a flooring that matches the wood trim or go with something more of a contrast?

The trend is to go with something more contrasting in color. Try using a different type of wood all together? Then you can pull in the door trim and floor color with accent pieces such as end tables, stools, chairs. picture frames. You will never be able to match it up perfectly especially if you are planning on using real oak flooring. Don't use more than 3 different types of wood and color in one space but mix it up, it will look great.